To hypothesize the least violent encounter I can imagine where the use of lethal force by the police would be justified:
If someone is advancing on you, a known explosives user (during the chase) who's from a region where the use of "suicide vests" is common, and refuses to stop, you without hesitation shoot to stop. And at as far a distance as you can.
The encounter could have been more violent on the part of the deceased, or since he killed a fellow officer it could have been an execution as all too often happens like recently in California. But the event was probably more confused than any of what I'd said here might imply.
All I can say that we know by inference is that the event was confused enough, and/or there were few enough police there, that his brother escaped---actually, I don't think we know that, the brother might have been let off before the stop---and has obviously successfully gone to ground. Likely into an apartment or home, and they're going to have to search house to house, apartment to apartment, could take quite a while assuming he is inside the 25 block? cordoned off area in Watertown. Not too familiar with that suburb, but I lived in Cambridge and surrounding mostly urban suburbs for a dozen years, it's likely a densely populated area. Even with a maximum effort by all it could drag on for more than a day, or he could get flushed out a minute from now.
ADDED: while all current accounts from the media are highly suspect, this: http://boston.cbslocal.com/2013/04/19/report-boston-marathon... would fit in what else we've heard or can discern:
"According to WBZ-TV’s Joe Shortsleeve, MBTA transit police intercepted the Mercedes in Cambridge and followed it.
"A source told Shortsleeve the brothers lost control of the car and crashed it. A gunfight with police erupted and an MBTA police officer was shot and seriously wounded.
"Miller reported that Tamerlan Tsarnaev threw a bomb at police as he approached them and that’s when officers shot and killed him.
"Shortsleeve’s source said Dzhokhar Tsarnaev then jumped back in the Mercedes, drove over his brother’s body, threw bombs at police and crashed again. He ran off, firing a weapon and that sparked the massive manhunt in Watertown."